This　work　aims　to　identify　ways　for　the　equivalent　material　parameters　of　metal-rubber　(MR),　as　well　as　the　establishment　of　theoretical　and　numerical　methods　for　sandwich　cylindrical　shells　with　metal-rubber　core　(SCSMR)　under　thermal　conditions.　To　achieve　this　goal,　the　first-order　shear　deformation　theory　and　Hamiltonian　principle　are　used　to　derive　equations　and　expressions　that　consider　temperature　variations　and　elastic　boundary　constraints.　This　leads　to　the　development　of　a　novel　dynamic　model　for　sandwich　cylindrical　shell　structures　in　a　thermal　environment.　Furthermore,　the　study　analyzes　how　vibration　frequencies　are　affected　by　boundary　spring　stiffness　and　axial　truncation　number　of　displacement-permitted　functions　using　the　Jacobi-Ritz　method.　The　impact　of　aspect　ratio,　core　layer　thickness　ratio,　and　temperature　on　the　vibration　frequencies　of　SCS-MR　is　discussed.　The　results　indicate　that　temperature　slightly　affects　the　frequency　of　SCS-MR.　As　the　aspect　ratio　increases,　the　vibration　frequency　tends　to　decrease,　irrespective　of　the　circumferential　wave　number.　However,　the　circumferential　wave　number　plays　a　considerable　role　on　vibration　frequency　associated　with　the　core　layer　thickness　ratio.